In a wireless communications system, the air interface typically involves a mobile station communicating with a base station over the airwaves. For example, the most common standard for wireless communications in the world is the Global System for Mobile communications (GSM). In one specific implementation, GSM utilizes two bands of 25 MHz, which have been set aside for system use. The 890-915 MHz band is used for mobile station to base station transmissions (reverse link), and the 935-960 MHz band is used for base station to mobile station transmissions (forward link). The GSM protocol uses frequency division duplexing and time division multiple access (TDMA) techniques to provide base stations with simultaneous access to multiple users. Transmissions on both the forward and reverse link are made at a channel data rate of 270.833333 Kbps, using binary Gaussian Minimum Shift Key (GMSK) modulation. Additionally, each link contains traffic channels and control channels. The traffic channels carry the digitized voice or user data. The control channels carry network management or control information such as the frequency correction channel (FCCH).
When a mobile station is powered on, it must first perform a power scan across all the control channels, to identify the channel with the strongest signal. The mobile station then tunes into the strongest channel to locate the FCCH. FCCH carries a frequency correction burst, which occupies time slot 0 for the very first GSM frame and is repeated every ten frames within a control channel multiframe. The FCCH burst allows each mobile station to synchronize its reference local oscillator or voltage controlled oscillator (VCO) to the exact frequency of the base station.
However, the VCO in a mobile station is usually not as robust as the VCO at the base station. Consequently, the frequency will fluctuate with the temperature of the VCO, in addition to other factors, such as aging, that will also contribute to the fluctuation but in a less significant amount. The frequency fluctuation will accumulate over time resulting in degrading the performance of the mobile station's receiver. An automatic frequency control (AFC) subsystem is an important component of a receiver for performance stability. For example, the GSM 11.10 specification requires a mobile station to maintain a carrier frequency to within 0.1 parts per million (ppm) of the base station's reference frequency, in other words, 0.1 ppm compared to the signals received from the base station. Although, the prior art Maximum Likelihood method can be used to obtain reliable frequency tracking, but it requires a long data stream and complex computation. Similarly, the prior art Time Domain Bias method can also be deployed for estimating frequency offset, but it needs a high sampling rate as well as a long data stream. Accordingly, the AFC subsystem in the receiver of a mobile station needs a reliable, simple, and effective frequency tracking technique to minimize frequency error to an acceptable level.